Coherent transmission from distributed wireless transmitters

ABSTRACT

In one aspect, a distributed coherent transmission system enables transmissions from separate wireless transmitters with independent frequency or clock references to emulate a system where all the transmitters share a common frequency or clock reference. Differences in frequency and/or phase between transmitters are addressed by suitably precoding signals before modulation at one or more of the transmitters based on a synchronizing transmission from one of the transmitters (e.g., a master transmitter) received at a corresponding receiver sharing the frequency or clock reference with each of the one or more transmitters. Such a distributed coherent transmission system can allow N single-antenna transmitters with independent frequency or clock references to emulate a single N-antenna Multi Input Multi Output (MIMO) transmitter, or implement schemes such as distributed superposition coding or lattice codes that require coherence across separate transmitters.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application61/543,832, filed on Oct. 6, 2011, (Attorney Docket 70009-D13P01; ClientCase 14965) the contents of which are incorporated herein by reference.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with government support under contract numberCCF-0728645 awarded by the National Science Foundation. The governmenthas certain rights in the invention.

BACKGROUND

This invention relates to coherent transmission from distributedwireless transmitters. In particular, in some examples, thesetransmitters are access points (APs), for instance in 802.11, basestations, for instance in cellular networks, relay stations, or otherwireless nodes.

Communication capacities of conventional wireless networks, such as802.11 or cellular networks, can be limited by interference. Forexample, the wireless medium is shared, and as a result, if two nearbydevices transmit simultaneously, their transmissions typicallyinterfere, preventing either device from delivering its packet. Recentadvances in wireless technology have resulted in empirical wirelesssystems such as SAM, IAC and beamforming. These systems havedemonstrated that concurrent transmissions across different transmittersin the same interference region are possible. The throughput in wirelessnetworks employing these systems can be doubled or tripled.

However, such systems remain limited by the maximum number of antennason an individual node, and cannot continuously scale the throughput asmore transmitters join the systems. Conventional wireless networks, forexample, 802.11 and cellular systems, may alleviate this problem byusing all available channels or employing sectorized antennas. However,such techniques provide only a small constant gain that does not scaleas the number of users increases. Furthermore, simply adding additionaltransmitters does not improve user throughput, because thesetransmitters interfere with each other.

There is a need for a wireless networking system that can scalethroughput linearly as the number of users increases, yielding a fullyscalable wireless network.

SUMMARY

In one aspect, in general, a distributed coherent transmission systemenables transmissions from separate wireless transmitters withindependent frequency or clock references to emulate a system where allthe transmitters share a common frequency or clock reference. Atechnical problem with such an architecture is that the oscillatorfrequencies of the individual transmitters (i.e., those used tomodulate/demodulate signals) are unlikely to be exactly the same fromtransmitter to transmitter, which can result in phase synchronizationproblems. For example, a difference as small as 100 Hz in the oscillatorfrequencies of two transmitters can cause a phase difference of it πradians in the signals transmitted by the two transmitters after a shortperiod of 5 ms. Such a phase difference can cause significantdegradation in the ability of the two transmissions to remain coherenteven across the duration of a single packet. This problem is alleviatedby compensating for frequency and/or phases differences betweentransmitters by suitably precoding signals before modulation at one ormore of the transmitters.

In various examples, the transmitters are access points (APs), forinstance in 802.11, base stations, for instance in cellular networks,relay stations, or other wireless nodes. In the rest of this document,unless explicitly indicated otherwise, the term transmitter is usedbroadly to refer to any of these kinds of transmitting nodes.

In another aspect, in general, such a distributed coherent transmissionsystem is part of a distributed MIMO architecture. In such a distributedMIMO architecture multiple individual transmitters emulate a singlemulti-antenna MIMO transmitter without requiring a common frequency orclock reference to be available to all transmitters. In some examples,the transmitters are able to communicate with each other usingrelatively high speed connectivity such as a wired backhaul (forexample, in 802.11 APs, or cellular base stations) or a wireless medium(for example, bluetooth, IR, 802.11 in mobile devices using a cellularuplink), and use such connectivity to exchange the data they need tocommunicate to the receivers, as well as some minimal controlinformation. The transmitters can then utilize traditional MIMOtechniques to perform, for instance, beamforming, or nulling, atmultiple receivers.

In another aspect, in general, such distributed coherent transmissionenables independent transmitters to implement a variety of schemes inthe information theory literature that assume that such independenttransmitters share a common frequency or clock reference. Such schemesmight include, for instance, lattice codes in a wireless mesh network,superposition coding on a wireless uplink, interference alignment acrossdistributed transmitters, or distributed dirty paper coding/cognitiveschemes from independent transmitters.

In some examples, channel estimates from the transmitters to receiversare formed based on coordinated transmissions from the transmitters(i.e., including compensation for frequency and/or phase differences)with channel-related information being returned from the receivers. Suchchannel information may be used at each of the transmitters to formcombinations of data to direct transmission to particular receivers, forinstance, using a distributed MIMO approach (allowing the multipletransmitters to perform, say, beamforming or nulling, at one or morereceivers). In some examples, channel estimates from the transmitters tothe receivers are computed by the receivers using transmissions from thetransmitters, and explicitly communicated back to the transmitters. Inother examples, channel estimates from the transmitters to the receiversare formed or updated based on reverse transmissions from the receiversto the transmitters using a reciprocity approach to determine channelcharacteristics from the transmitters to the receivers. In yet otherexamples, a combination of channel estimation approaches is used, forexample, obtaining initial channel estimates from transmitters toreceivers by explicit communication from receivers, and updatingexisting channel estimates from transmitters to receivers based ontransmissions (e.g., acknowledgements) from the receivers to thetransmitters.

In another aspect, in general, a system enables a distributed set oftransmitters to emulate a multi-antenna transmitter approachingperformance achievable with a common oscillator frequency. In someexamples, this is accomplished by one or more slave transmitters usingtheir respective receiver modules to monitor the transmissions of amaster transmitter. The monitored transmissions of the mastertransmitter are used by the receive module of each slave transmitter toestimate a characteristic (e.g., a time varying part of a phase offsetbetween oscillators) between the master transmitter and the slavetransmitter. The monitored transmission from the master transmitter,along with the estimated channel characteristic is used by each slavetransmitter's receiver module to determine an oscillator frequencyoffset (and optionally phase offset) between the oscillator of themaster transmitter and the oscillator of the slave transmitter. Thedetermined oscillator frequency offset and phase offset at each slavetransmitter is used by the slave transmitter's transmitter module tocompensate transmissions.

In another aspect, in general, a method for operating a slavetransmitter to provide coordinated transmission with a mastertransmitter includes forming a signal for concurrent modulation from theslave transmitter with a transmission of the signal from the mastertransmitter. An estimate of a time-varying phase offset between amodulation frequency of a transmission from the master and a frequencyreference at the slave transmitter based on transmissions received atthe slave transmitter from the master transmitter is maintained at theslave transmitter. The signal is modified prior to modulation accordingto the estimate of the time-varying phase offset and then modulatedaccording to the frequency reference at the slave transmitter. Thesignal modulated at the master transmitter is transmitted from themaster transmitter and concurrently with the transmission of themodulated modified signal from the slave transmitter.

In another aspect, in general, a slave transmitter estimates the changein phase offset at any receiver relative to signals from a mastertransmitter based on transmissions from the master transmitter receivedat the slave transmitter. Estimating the change in phase offset includesdemodulating a transmission from the master transmitter, and comparingthe demodulated transmission to expected demodulated values.

In some examples, the transmission from the master transmitter includespreamble of a transmission of the signal from the master transmitter.

In another aspect, in general a slave transmitter monitors a frequencyoffset relative to a master transmitter while concurrently transmittingwith the master transmitter by coordinating periods of transmission andperiods of silence during joint packet transmission.

In another aspect, in general, a slave transmitter monitors a frequencyand/or phase offset relative to a master transmitter whilesimultaneously transmitting with the master transmitter by using asubset of antennas on the slave transmitter for cancelling theinterference from simultaneous transmission.

In another aspect, in general, a slave transmitter and mastertransmitter each continuously track channel estimates to a receiverwithout requiring periodic communication of channel information from thereceiver.

In some examples, the approach includes forming a signal for concurrentmodulation from the slave transmitter with a transmission of the signalfrom the master transmitter, maintaining an estimate of a time-varyingphase offset between a transmission from the master and a transmissionat the slave based on transmissions received at the slave transmitterfrom the master transmitter and modifying the signal prior to modulationaccording to the estimate of the time-varying phase offset; andmodulating the modified signal according to the frequency reference atthe slave transmitter.

In some examples, the approach includes concurrently transmitting thesignal modulated at the master transmitter from the master transmitterand the modulated modified signal from the slave transmitter.

In some examples, the data carried by the transmissions from the masterand slave transmitters is the same, and the slave transmitters (andpotentially the master) modify their transmitted signal(s) to increasethe strength (SNR) of the signal at a particular receiver.

In some examples, the data carried by the transmissions from the masterand slave transmitters is intended for different receivers, and can bedifferent, and the master and the slave transmitters modify theirtransmitted signals to allow each of their intended receivers to receivetheir intended data without interference from the other transmissions.

In some examples, acknowledgments from receivers are utilized fortransmission from a previous data packet to constantly update channelestimates to the receiver and for allowing the master and/or slavetransmitters to modify their transmitted signals prior to modulation atboth master and slave transmitters.

In another aspect, in general, a master transmitter includes a firstoscillator for operating at a first oscillator frequency, a firsttransmitter module for transmitting symbols, the first transmittermodule being coupled to the first oscillator for operating at the firstoscillator frequency a slave transmitter, each slave transmitter of theone or more slave transmitters including a second oscillator whichoperates at a second oscillator frequency a receiver module forreceiving transmissions from the master transmitter, the receiver moduleoperating at the second oscillator frequency and including a phase andfrequency offset tracking module for determining a frequency offsetbetween the first oscillator frequency and the second oscillatorfrequency based on the transmissions received from the mastertransmitter, and a second transmitter module for transmitting symbols,the second transmitter module operating at the second oscillatorfrequency and including a phase and frequency offset compensation modulefor compensating for the frequency offset before transmitting symbols.

DESCRIPTION OF DRAWINGS

FIG. 1 a is a master transmitter.

FIG. 1 b is a slave transmitter.

FIG. 2 is a block diagram of a model of baseband transmission paths.

DESCRIPTION 1 Overview

The system described herein allows N single-antenna transmitters withindependent frequency and clock references to emulate a system where theN transmitters have access to a common carrier reference with aconsistent phase and frequency across access points. This allows the Nsingle-antenna transmitters to emulate, for instance, a single N-antennamultiple-input multiple-output (MIMO) transmitter. The emulatedN-antenna MIMO transmitter can transmit N concurrent streams that do notinterfere with each other, delivering N concurrent streams to N users bybeamforming, nulling, or more general Multiple-Input-Multiple-Output(MIMO) techniques, for instance, nulling at particular receivers whiletransmitting fewer than N streams. Such a system could be deployed, asan example, in a large room (e.g., a conference center) or an outdoorsetting (e.g. a dense urban area) to provide tens or hundreds oftransmitters that enable concurrent transmission of a commensuratenumber of data streams without interference. More generally, some or allof the multiple transmitters and some or all of the user devices mayhave multiple antennas.

In various examples discussed below, the “transmitters” (or “sourcestations”) can be various types of nodes in a communication network thatfunction, at least in part or at some times, as transmitters. The“transmitters” generally include transmitter and receiver components,and are referred to as “transmitters” in their role as transmitting oneor a subset of the coherent transmissions to client “receivers” (or“destination stations”), which also generally include transmitter andreceiver components, and a referred to as “receivers” in their role asreceiving the multiple coherent signals from multiple “transmitters”.Such transmitters can include, without limitation, wireless Ethernetinfrastructure access points (APs), for instance in 802.11n accesspoints, wireless repeater stations, base stations, for instance incellular networks, relay stations, or other wireless nodes. In the restof this document, unless explicitly indicated otherwise, the terms“transmitter” and “access point” is used broadly to refer to any ofthese kinds of nodes that transmit to other wireless stations.

For a client receiver (referred to simply as the “client” or “receiver”in some instances below) to decode its intended signal withoutinterference, it is desirable that the N−1 signals intended for theother clients cancel (i.e., destructively interfere with) each other atthat client. For cancellation to occur, each transmitter controls thephase (and magnitude) of its transmitted signals such that cancellationis achieved at every unintended client, for every transmitted symbol.Controlling the phase between transmitted signals is relatively simplefor a single N-antenna transmitter when all of the transmit antennasshare the same oscillator. In contrast, in a distributed setting, thetransmit antennas are on different transmitters, and hence each transmitantenna is connected to a different oscillator. Different oscillatorsnaturally have unknown phase shifts with respect to each other.Furthermore, since different oscillators never have the same exactfrequency, and since different transmitters might independently chooseto turn off their oscillators, for instance, to reduce operating power,these phase shifts change over time. Enforcing the consistent phasesynchronization in this distributed setting is highly challenging.

It should be understood that although certain discussion below focuseson transmitters each with a single antenna, the approaches areapplicable where some or all of the transmitters have multiple antennascontrolled according to common oscillators. In such cases, within onetransmitter, the signals transmitted from that transmitter's antennasnaturally maintain consistent phase relative to one another by virtue ofthe use of the common oscillators. For example, N 2-antenna accesspoints could therefore emulate a 2N-antenna access point.

Referring to FIGS. 1 a and 1 b, in an illustrative example (e.g., N=2transmitters, recognizing that the approach is applicable to much largernumbers of access points and client receivers) a single antenna mastertransmitter 102, a single antenna slave transmitter 104, and two singleantenna client receivers 106, 110 are configured to communicatewirelessly over a shared medium. Note that the antennas as shown ascoupled to both transmitter and receiver sections at the devices, withcoupling and/or switching circuitry not shown. The master transmitter102 controls concurrent transmission of two data frames, X₁ and X₂, tothe two receivers, respectively. The signals emitted from the antennasof the master transmitter and the slave transmitter are synchronized toachieve the desired constructive and destructive interference at theantennas of the receivers.

In this example, both the master transmitter and the slave transmitterhave access to the data frames X₁ and X₂ that are to be transmitted tothe receivers. For instance, each transmitter may have received the dataframes over a wired network (or wireless network, say on the same ordifferent frequencies) linking the transmitters.

Referring to FIG. 1 a, to transmit the two frames, the mastertransmitter 102 receives a data frame (i.e., receives the data packetfor the payload to be transmitted in the frame) and provides the data toa master parallelization module 112. The master parallelization module112 parallelizes the stream of symbols into K sequences, for example X₁to x_(1,0) ^((k)), x_(1,1) ^((k)), x_(1,2) ^((k)), . . . for k=0, . . ., K−1, of values represented by complex values (symbols) from a fixedconstellations (e.g., QAM constellations). As outlined below, each ofthe sequences will be modulated to a different frequency in anOrthogonal Frequency Division Multiplexing (OFDM) approach.

The master parallelization module 112 outputs the mapped symbols x_(1,0)^((k)), x_(1,1) ^((k)), x_(1,2) ^((k)), . . . for the first receiver andthe mapped symbols x_(2,0) ^((k)), x_(2,1) ^((k)), x_(2,2) ^((k)), . . .for the second receiver to a master pre-coding module 114 in a mastertransmit portion 103. The master pre-coding module 114 also receiveschannel transfer functions representing the channels from the transmitantennas of each transmitter 102, 104 to the (receive) antennas of eachof the receivers 106, 110. Since there are two transmitters and tworeceivers in the system of FIG. 1, there are four channel transferfunctions for each: h₁₁, h₁₂, h₂₁, h₂₂. h₁₁ is the channel transferfunction from the master transmitter 102 to the first receiver 106. Ingeneral, the transfer function for each frequency component is aseparate complex number, but the k-dependence is omitted from thenotation for clarity and/or the channel h_(ij) can be considered to be aK-dimensional complex vector. h₂₁ is the channel transfer function fromthe master transmitter 102 to the second receiver 110. h₁₂ is thechannel transfer function from the slave transmitter 104 to the firstreceiver 106. h₂₂ is the channel transfer function from the slavetransmitter 104 to the second receiver 110.

Considering a single frequency component k (and omitting the kdependence in the notation below), the master pre-coding module 114pre-codes the mapped symbols based on the channel transfer functionsh₁₁, h₁₂, h₂₁, h₂₂ to produce the combined precoded symbols y_(1,0),y_(1,1), . . . such that the mapped symbols are received in combinationwith the transmission from the slave transmitter at the antenna of thefirst receiver 106 to provide x_(1,0), x_(1,1), . . . and cancelx_(2,0), x_(2,1), . . . while providing x_(2,0), x_(2,1), . . . at theantenna of the second receiver 110 and cancelling x_(1,0), x_(1,1), . .. . Conventional MIMO techniques are implemented by the masterpre-coding module 114 and will not be discussed further herein.

The output of the master pre-coding module 114 is provided to a mastermodulation module 116 which converts each of the mapped, pre-codedsymbols into a time domain waveform. At least conceptually, a basebandtime waveform is formed such that effectively the k^(th) component ismodulated to a frequency kγ₁, where the factor γ₁ depends on thesampling rate of the conversion to a time signal in the modulator and issubstantially proportional to the desired sampling frequency γ_(s). Themaster modulation module is driven by the master modulator 116, whichproduces a carrier signal substantially at the desired carrier frequencyω_(c), and more precisely representing modulation of the k^(th) input bythe complex sinusoidal signal exp j((ω₁(t)+kγ₁(t))t) such thatω_(i)(t)≈ω_(c), γ_(i)(t)≈γ_(s), and ω_(i)(t) and γ_(i)(t) may be slowlyvarying. The output of the master modulation module 116 is a time domainsignal including a sum of N orthogonal sub-carriers, each sub-carriercarrying one symbol. The output of the master modulation module 116 isprovided to a master antenna 120.

Referring to FIG. 1 b, the transmit portion 105 of the slave transmitter104 transmits symbols in much the same way as the master access point102. However, as introduced above, the slave access point has a separateoscillator 144, which is used to modulate transmissions from the slaveaccess point. The slave oscillator 144 produces a carrier signalsubstantially at the desired carrier frequency ω_(c), and more preciselyrepresenting the complex sinusoidal signal exp j((ω₂(t)+kγ₂(t))t) suchthat ω₂(t)≈ω₁(t)≈ω_(c), γ₁(t)≈γ₂(t)≈γ_(s), typically with ω₁(t)≠ω₂(t),and γ₁(t)≠γ₂(t) These differences are explicitly accounted for asdescribed below.

At each of the master and slave, a demodulator on the received pathmakes use of the same oscillator (142, 144), and therefore differencesbetween the oscillators are manifested both on the receive and transmitpaths of the access points.

In order to emit coordinated (e.g., coherent) transmissions from themultiple access points, two issues are addressed:

-   -   a. Synchronizing transmissions from multiple access points such        that they maintain a consistent relative phase within a single        simultaneous frame transmission; and    -   b. Determining channel estimates, which are consistent with the        consistent relative transmission phases, between access points        and clients such that MIMO techniques can be applied to precode        transmissions such that multiple data streams can be transmitted        to their intended destinations during the simultaneous        transmissions.

For the first of these issues, it is important to note that simplycorrecting for oscillator frequency may result in a consistent phasewithin one frame transmission. However, small errors in estimate of thedifference in oscillator frequency can result in the relative phase ofthe simultaneous transmissions varying from frame to frame, therebymaking it difficult to maintain an estimate of the channels from theaccess points to the clients that are valid for long enough to beuseful.

Therefore, the approach to synchronization addresses both compensationfor frequency offset and phase offset at each frame transmission andadjusting the phase for successive symbols in the transmission of theframe. The general approach is to make use of a synchronizing frametransmission from a lead access point that is received by one or moreslave access points shortly before the simultaneous transmission toclients by the lead and the one or more slave access points. Generally,and as explained in more detail below, the slave access points use thereceived synchronizing transmission from the lead access point tocompensate their simultaneous transmissions to achieve their consistentfixed relative phase to the lead access point.

The issue of determining channel estimates from the access points to theclients can be addressed in a variety of ways. Some approaches make useof clients that are aware that transmissions emit from multiple accesspoints, and with suitable coordination provide feedback to the accesspoints to permit estimation of the downlink channels and application ofMIMO techniques for subsequent downlink transmissions from the accesspoints.

2 Principles of Operation

Before discussion of specific embodiments, a number of principles ofoperation are described in a specific context of two single-antennaaccess points, one a master and one a slave, which communicate with twosingle-antenna clients. It should be understood that this is a verysimple illustrative example, and that the principles of operation extendnaturally to more than two access points, and to access points andclients each with multiple antennas.

Referring to FIG. 2, signal paths from between access points and clientscan be decomposed into their equivalent baseband components as shown.FIG. 2 shows input signals (i.e., complex values) s₁ and s₂, which aretransmitted from the lead access point 102 and slave access point 104such that they combine to form (scaled versions of) desired signals x₁and x₂ at clients 106 and 110, respectively. Signals s₁ and s₂ arerepresentative values at a particular frequency (k), at a time offsetwithin a transmission frame—but for clarity of explanation the frequencyand time dependence are omitted from the notation.

The input signals are determined using conventional MIMO techniquesbased on channels estimates between the access points and the clients,for examples as (s₁,s₂)^(T)=H⁻¹ (x₁,x₂)^(T), or more generally a powerlimited version, for example (s₁,s₂)^(T)=βH⁻¹ (x₁,x₂)^(T) where β ischosen to satisfy power constraints at the master and/or slave accesspoints. One aspect discussed below is an approach to determiningsuitable entries for the channel matrix H such that the signals s_(i)yield the desired combinations at the clients. The application of H⁻¹ isnot shown in FIG. 2.

The components of the signal paths are shown in detail in FIG. 2,however, in operation it is not necessary to consider each componentindividually, and the system in FIG. 2 does not necessarily correspondto the physical structure, while still providing a basis for describingthe procedures used.

At the lead access point 102, in the transmit path, the hardware (e.g.,amplifier, antenna, antenna-air interface, etc.) introduces a complex(generally time-invariant) gain t₁ ^(AP). Note that FIG. 2 illustrates asingle frequency component, and therefore the gains shown in the figureare generally dependent on the frequency. Similarly, the receive pathincludes a gain r₁ ^(AP). Note that in general, the (complex) gains onthe transmit and receive paths are not equal. The slave access point 104similarly has transmit and receive path gains t₂ ^(AP) and r₂ ^(AP),respectively.

In addition, as introduced above, the receive path at a slave includes atime varying, unit gain, “rotating” phase component, which can beapproximated as d₂ ^(AP)(t)≈exp j(θ_(n)+(t−τ_(n))Δω_(n)) near timeτ_(n), which represents the mismatch between the oscillator frequencyand the sampling frequency at the slave access point relative to themaster access point. Because the same oscillators and sampling clocksare used on the output path of the slave access point, the output pathalso includes a rotating phase component d₂^(AP)(t)≈exp(−j(θ_(n)+(t−τ_(n))Δω_(n))), with rotating phase componentsthat are rotating in the opposite direction than on the receive path.(Note that the term Δω_(n) is in general dependent on the frequencycomponent k, for example reflecting both the oscillator frequencyoffset, as well as factors that depend on the sampling frequency for themodulation and demodulation.)

As illustrated, the clients similarly have transmit and receive pathgains, t_(i) and r_(i), as well as rotating phase components d_(i) (t)that account for the mismatch of the client oscillators and samplingclocks.

The over-the-air paths between access points i and j are shown as a_(ij)^(AP) and are assumed to be reciprocal. Similarly, the reciprocal pathbetween access point i and client j is shown as a_(ij).

2.1 Slave Transmit Compensation for Oscillator Frequency and PhaseOffset

Referring again to the slave access point 104, when the slave accesspoint receives a transmission from the master access point, known values(“pilot symbols”) in the transmission allow the slave to determine amagnitude and a phase of the path from the master to the slave. Thispath is considered to have a relative constant part with gain r₂ ^(AP)a₁₂ ^(AP) t₁ ^(AP) as well as the part d₂ ^(AP) (t), which as introducedabove is modeled locally as d₂ ^(AP)(t)≈exp j(θ_(n)+(t−τ_(n))Δω_(n)).When the slave receives a transmission at time τ_(n), it cannotdistinguish between the phase introduced by relatively constant part,but can approximate the total phase as ∠(d₂ ^(AP)(t)r₂ ^(AP)a₁₂ ^(AP)t₁^(AP))=ψ_(n)+(t−τ_(n))Δω_(n).

On the transmit path, the slave access point includes phase adjustmentelements b and c(t) (which are implemented prior to the IDFT andmodulation in the transmit path), that introduces an opposite phase ofthe expected time varying phase difference introduced on the output pathby d₂*^(AP)(t). Phase adjustment elements b and c(t) each have unitmagnitude and together introduce the opposite phase of d₂*^(AP)(t). Attime τ₀, b is initialized to unity, and c(t) is set such to unitmagnitude with ∠c(t)=(t−τ₀)Δω₀. Note that a value s₂ transmitted shortlyafter τ₀ experiences a gain d₂*^(AP)(t)c(t)b, which is approximately aconstant with unit magnitude and phase −θ₀, prior to passing to thetransmit path via the t₂ ^(AP) block shown in FIG. 2. (Note that therelative phase of the signal provided to the transmit path at the slavevia the t₂ ^(AP) block as compared to the phase of the signal providedto the transmit path at the master via the t₁ ^(AP) block is therefore−θ₀+∠(r₂ ^(AP)a₁₂ ^(AP)t₁ ^(AP))=ψ₀=2θ₀.

At a subsequent time, τ_(n), when the slave access point receivesanother transmission from the master, the estimator determines newestimates ψ_(n) and Δω_(n) and updates b and c(t) such that ∠b=ω_(n)−ψ₀and ∠c(t)=(t−τ_(n))Δω_(n). Note that the change in phase of theoscillator θ_(n)−θ₀ is equal to ψ_(n)−ψ₀ (assuming the phase of r₂ ^(AP)a₁₂ ^(AP) t₁ ^(AP) has remained constant), therefore a new value s₂transmitted shortly after τ_(n), (i.e., after the blocks b and c(t) areupdated) again experiences a constant gain d₂*^(AP)(t) c(t)b, which isapproximately a constant with unit magnitude and phase —θ₀, prior topassing to the transmit path via the t₂ ^(AP) block. (Note that as atthe time shortly after time τ₀, with the updated blocks b and c(t) andtime τ_(n), the relative phase of the signal provided to the transmitpath at the slave via the t₂ ^(AP) block as compared to the phase of thesignal provided to the transmit path at the master via the t₁ ^(AP)block is maintained as −θ₀+∠(r₂ ^(AP)a₁₂ ^(AP)t₁ ^(AP))=ψ₀−2θ₀.)

2.2 Coherent Transmission from Master and Slave Access Points

Coherent transmission of values s₁ and s₂ from the master and the slaveaccess points, respectively, is accomplished by the master access pointfirst sending a synchronizing transmission (i.e., a sequence thatincludes known symbols) to the slave at a time τ_(n). As describedabove, the slave access point updates its compensation terms accordingto ψ_(n) and Δω_(n) from that received synchronizing transmission.

At a known time delay, at time τ_(n)+Δτ, the master and the slaveconcurrently transmit s₁ and s₂ respectively (i.e., these symbols aretransmitted as part of a larger frame). These transmissions pass to thetransmit blocks t₁ ^(AP) and t₂ ^(AP) at a fixed relative phasethroughout the transmission, so there is no phase rotation between thetwo signals. Furthermore, successive transmissions experience the samerelative phase as outlined above (i.e., relative phase ψ₀−2θ₀). Thislatter feature is significant in that channel estimates from the slaveaccess point to the clients are not affected by change in the slaveoscillator phase and frequency offsets from the master.

It is important to recognize that the slave access point may experiencea delay in detecting the transmission from the master access point. Forexample, suppose it detects the transmission δτ late, and then makes itstransmission at time τ_(n)+τ+δτ. Because of the late detection of theknown symbols in the transmission form the master, the slave's estimateof the phase is increased by δψ, and the increase in the phase of thecompensation term b exactly compensates for the late transmission fromthe slave, thereby the approach is essentially insensitive to the amountof detection delay.

2.3 Slave Receiver Compensation for Oscillator Frequency and PhaseOffset

On the receive path at the slave access point, a similar compensationfor oscillator phase and frequency offset can be accomplished byeffectively multiplying the received signal by b*c*(t). For example, inthe time vicinity of τ₀ when a signal is received (e.g., from a client),the gain of the compensated path b*c*(t)d₂ ^(AP) has approximately unitmagnitude and phase θ₀. Again, in the time vicinity of a subsequentupdate at time τ_(n), the phase of this compensated path remainsapproximately θ₀.

2.4 Access Point to Client Channels

The effective baseband signal path from the master access point (j=1) toclient i is g_(i1)=d_(i)(t)r_(i)a_(i1)t₁ ^(AP). If the client uses knownvalues in the transmission to compensate for its oscillator phase andfrequency offsets, then the effective channel is {tilde over(g)}_(i1)=r_(i)a_(i1)t₁ ^(AP)

Assuming that the slave access points compensate for their rotatingtransmit phase relative to the master as described above, and thecorrection terms remain accurate, the effective phase-corrected basebandsignal path from the slave access point j to client i (i.e., taking intoaccount the compensation of the input in the b and c(t) blocks) isg_(ij)=d_(i)(t)r_(i)a_(ij)t_(j) ^(AP)d_(j)*^(AP)(τ₀), whered_(j)*^(AP)(τ₀)=exp(—jθ₀) is the effect of the initial phase measured atthat slave access point and recorded at slave access point j. Again, ifthe client uses known symbols in the transmission to compensate for itsoscillator phase and frequency offsets, then the effective channel is{tilde over (g)}_(ij)=r_(i)a_(ij)t_(j) ^(AP)d_(j)*^(AP)(τ₀).

It is important to note that the channel estimates h_(ij), which formthe elements of the matrix H, are only required to be known to within a(complex) proportionality β_(i), which depends on the destination clienti. In the discussion below this proportionality constant defined suchthat h_(ij)=α_(i)g_(ij).

3 Coherent Transmission from Slave Access Points

Steps that lead up to concurrent transmission from the multiple accesspoints consistent with the principles described above is therefore asfollows. Note that there is an underlying assumption in these examplesthat the access points are linked by high-capacity backend channel(e.g., gigabit wired Ethernet). Frames intended for clients aredistributed to all the access points through the shared backendchannels, and the desired precoding of the frames (e.g., H⁻¹) iscoordinated via the backend channel as well.

In this example, it is assumed that one access point has already beenidentified as the master access point, for example, because it was thefirst to power up or because it is particularly configured to act as themaster. In this example, we assume that there are N−1 slave accesspoints (numbered 2, . . . , N with the master being numbered 1), eachwith one antenna, which will participate in the simultaneoustransmissions.

Initialization:

1) For each slave access point n=2, . . . , N, at a time τ₀ ^((n)) themaster sends an initial transmission to that slave, based on which theslave determines an initial phase offset ψ₀ ^((n)) for each frequencycomponent (i.e., ψ₀ ^((n))) can be represented as a vector for all thefrequency components) which it records. Note that these initializationsare not in general concurrent for all the slave access points.

Concurrent Transmission from Access Points:

2) At a time τ₁, the master transmits a synchronization frame directedto each of the slaves. We assume that via backend channel and/or viaidentifying information in the synchronization frame the slavesdetermine the desired frames S_(n) to transmit from each of the accesspoints.3) At each of the slave access points n=2, . . . , N:

-   -   a) the transmission from the master is detected (recognizing        that each slave may detect that transmission at a slightly        different delay)    -   b) the slave access point determines a new phase offset ψ₁        ^((n)) and frequency offset Δω₁ ^((n)) (i.e., estimates for each        frequency component, although the estimates of Δω₁ ^((n)) may        make use of information from a range of frequency component)        based on which it configures it correction elements b and c(t).        c) a fixed delay after detection of the transmission from the        master, the slave transmits the frame S_(n) via its configured        correction elements b and c(t)

As introduced above, the result of this correction is that each accesspoint effectively maintains a fixed phase (provided to the transmitcomponents t_(j) ^(AP)) relative to the master.

Steps 2 and 3 are repeated in subsequent transmissions.

Note that step 2 is described above as a transmission of an entire frameto the slave. It should be understood that a preamble of a frame (e.g.,a 802.11n legacy preamble) can be sufficient for the slave tosynchronize and then join in with the transmission from the master, suchthat the preamble is transmitted from the master and the body of theframe is transmitted from the master and the slave. Such an approach canbe compatible with wireless Ethernet standards, for example, in thatautomatic gain control and channel estimation is not performed untilafter the legacy preamble.

3.1 Multiple Antenna Access Points

Note that although the discussion addresses single-antenna accesspoints, multiple antenna access points are addressed by making use ofthe observation that such multiple antennas make use of a commonoscillator. Therefore, the procedures described above for one antennacan be extended to multiple antennas by making use of one antenna forreceiving the synchronizing transmission from the master, orequivalently, a fixed combination (weighting) of multiple antennas, forexample, providing a desirable receive sensitivity in the direction ofthe master access point. Each transmit stream is then compensatedindependently using the same estimated compensation terms (b and c(t)).

4 Client Feedback Based Channel Estimation

As discussed above, the master and slave access points can form coherenttransmissions by the master access point first sending a synchronizingtransmission and then at a fixed delay both master and slave sendingtransmissions to one or more clients.

Generally one approach to channel estimation involves a client receivingthe concurrent transmissions and being able to identify components ofthe transmission from each of the access points that include knownsymbols, thereby allowing it to estimate the channels from each of theaccess points, and report those channels to the access points, which inturn compose the overall channel matrix H, which is then inverted andused to determine the values s_(i) in subsequent transmissions.

One approach to permitting the client to identify the components fromeach of the access points is to interleave transmissions in time fromeach of the access points in a pattern known to the client such that atcertain times each access point transmits alone include a known symbol.Because the transmission includes only one access point transmitting ata time, the client can determine each channel separately.

Another approach is for each of the access points to send a differentset of linearly independent known values. For example, in the case oftwo simultaneous transmissions, if the master sends (s₁₁=z, s₁₂=z) andthe slave sends (s₂₁=z, s₂₂=−z), the client effectively receives(s₁₁{tilde over (g)}_(i1)+s₂₁{tilde over (g)}_(i2), s₁₂{tilde over(g)}_(i1)+s₂₂{tilde over (g)}_(i2)) from which it can solve for {tildeover (g)}_(i1) and {tilde over (g)}_(i2) to report back to the accesspoints. More generally, N_(c) linearly independent sequence of at leastN_(c) values are sent from multiple access points, and a clientdetermines the relative channels (i.e., the channels to within anunknown complex scale factor) from each of the access points.

Note that channels to multiple clients may be determined in this manner,with the transmissions to different clients being made at differenttimes, or optionally, the same transmissions from the access pointsbeing used by more than one client to estimate the channels.Furthermore, the sequence of transmissions with different subsets ofantennas may be interleaved for different clients.

5 Alternatives

5.1 Resynchronization within a Packet

The approaches described above enable slave access points to accuratelysynchronize their phase with the lead access point at the beginning ofdata transmission, and then use an estimate of their phase and frequencyoffset to the lead access point to account for phase rotation within apacket. Alone, such a technique can lead to accumulative errors in phasewithin a packet, thus reducing SNR at the receivers, although themagnitude of these errors is smaller than in the initial phase rotationas they only accumulate within a packet, rather than across packets. Ifoscillator offset estimates are sufficiently accurate, these errors willbe small enough that the SNR of the joint transmissions is unaffectedfor normal frame length. In this section, we describe techniques totrack and compensate for oscillator offset errors during the duration ofa frame, in cases where the errors are large enough to make asignificant impact on the received SNR of the joint transmissions.

One alternative enables slave access points to compensate for errors inphase synchronization even through the duration of a packet. The basicidea is that slave access points listen to the lead access pointstransmission, estimate their current channel to the lead access point,and recalibrate their estimate of the lead access point's oscillatorphase appropriately. The challenge with implementing this idea, however,is that slave access points cannot naively listen to the lead accesspoint's transmission while simultaneously transmitting themselves, asthe slave access points transmission power will overwhelm the ADCs ontheir receive chains. At least two different mechanisms can be used toenable slave access points to address this challenge, depending onwhether or not slave access points can cancel the power of their owntransmissions.

If the slave access points cannot cancel their own transmissions, whichcan happen when slave access points have only a single antenna, or whenslave access points have multiple antennas but cannot expend the powerto cancel their own signal (potentially because they are in a powerlimited regime), the access points use a scheme where slave accesspoints periodically remain silent, and the lead access point transmits aknown symbol during this silence to enable phase tracking. Specifically,the lead access point transmits a resync symbol every L data symbols.Slave access points do not transmit concurrently during this resyncsymbol. Instead, they compute the channel from the lead access pointusing this resync symbol, and use its difference from the channelcomputed using the previous resync symbol (or the synchronization headerin the case of the first resync symbol) to resynchronize phase.

It may seem that using only one resync symbol would lead to noisyestimates of the channel at the slave access points, thus reducing theiraccuracy of resynchronization. However, the channel estimates can bedenoised since it uses OFDM over a wideband channel. The phase rotationsacross OFDM subcarriers are correlated, and we can leverage thiscorrelation to denoise the phase rotations even with one OFDM resyncsymbol.

Specifically, the slave access points use a technique motivated by OFDMfine phase tracking. A slave access point uses each resync symbol toestimate the current channel to the lead access point for eachsubcarrier. It then computes the phase difference between this channeland the channel computed from the previous synchronization symbol, forall subcarriers. The phase difference computed per subcarrier, but fornoise, would lie along a line. This is because, as in standard finephase tracking, the carrier frequency offset (CFO) between the lead andslave access point produces the same phase shift across subcarriers,while the sampling frequency offset (SFO) produces a phase shiftproportional to subcarrier index. Thus, by fitting a line to the phaseoffsets, we can denoise the estimates of the phase change of the channel(from the lead access point to the slave access point) since theprevious synchronization. The values on the line are the actual denoisedphase changes for each subcarrier. These values can now be applied tothe current estimate of Δφ_(1i) ^(AP) for the corresponding subcarriers.

The value of L, i.e., the resync interval, depends on the maximumtolerable phase error, and the accuracy of frequency offset estimation.For an N×N system with a frequency offset error of 100 Hz, in order tosustain SNRs upto 25 dB, as required by an 802.11 system, it needs toinsert resync symbols every

$\sqrt{\frac{10^{- 2.5}}{N}} \times \frac{1}{100 \times 2\pi}$

seconds. For a 10×10 system in 802.11g, this translates to an overheadof 1 resync resymbol every 7 data symbols, i.e., just 14%, with theoverhead increasing only increasing as √{square root over (N)}.

Note that while a SIFS after the synchronization header is necessary, aSIFS after the resync symbol is not. This is because, for thesynchronization header, the slave access points need to compute thechannel and phase estimates from this header before they can starttransmitting. In contrast, in the case of a resync symbol, the slaveaccess points already have reasonable estimates that they can use fortransmitting their symbols, even as they compute the new estimates fromthe resync symbol in parallel.

The preceding mechanism enables slave access points to synchronize withthe lead access point even when they cannot cancel their owntransmissions, but requires them to obtain a reasonably good estimate ofthe initial frequency offset, and has overhead that increases, albeitslowly, with N. However, the system can take advantage of the ability ofslave access points to perform cancelation using (1) additionalcarefully placed transmit antennas (but not additional tx/rx chains inhardware), (2) arbitrarily placed antennas with associated tx/rx chains,or (3) calibrated circuits between transmit and receive antennas

The first case applies when each slave has a single transmit antenna andseparate transmit and receive antennas. In that case, the slave can usea second “cancellation” antenna whose separation from the receiveantenna is larger than the separation of the first transmit antenna fromthe receive antenna by half a wavelength. The second transmit antennatransmits the same signal as the first antenna, and the two signals willdestructively interfere at the receive antenna. This will allow thereceive antenna to receive signals from other transmitters (inparticular the master) even while it is transmitting its own signal.

The second case applies when slaves have multiple transmit antennas, andreceive antennas that could potentially be co-located with the transmitantennas. Let us consider a case with K transmitters, each with Mantennas, and K receivers, each with N antennas. In such a case, eachtransmitter can transmit upto M−1 streams for a total of K(M−1) streamsacross all transmitters, while still ensuring that slaves can receivewhile transmitting. This is achieved as follows: One transmit antenna ateach slave cancels the result of all the transmitted signals at one ofthe receive antennas on that slave (the slave might use more than one“cancelation” antenna in order to deal with any power mismatches betweenthe transmission power required at the “cancelation” antenna to cancelall the transmitted signals). Note that the cancelation need not beperfect, but just needs to be sufficient for the slave to acquire a goodenough signal from the master to perform frequency offset estimation.The slave can then use the signal received from the master on thisreceive antenna to perform frequency offset estimation from the master.Note that a single receive antenna is sufficient for the slave to trackfrequency offset from the master independent of the number of transmitantennas on the master (unlike in the case of full decoding where theslave would need as many receive antennas as the master uses totransmit). This is because all the transmit antennas on the master havethe same oscillator frequency and hence there is only a single parameterto be estimated at the slave. The slave can potentially use additionalreceive antennas (using up to L receive antennas for simultaneousreception will require L “cancelation” antennas) to take advantage ofchannel diversity or robustness from multiple measurements.

The third case applies where the slave AP hardware uses circulatorsbetween transmit and receive antennas, as well as calibrated circuitsbetween the different transmit and receive antennas to ensure that thetransmitted signals from the different transmit antennas cancel out at areceive antenna. This solution does not require any additional transmitantennas at the slaves.

In all cases described above, the slave access point can receive thelead access point's transmission without self-interference from its owntransmissions. However, the slave access point also needs to ensure thatthe lead access points transmissions are not interfered with bytransmissions from other slave access points. The new approach ensuresthis by exploiting the idea of OFDM pilots, typically used for receivertracking in single-user systems like 802.11. Only the lead access pointtransmits in the assigned OFDM pilot subcarriers. Using one or more ofthe cancelation techniques described above, each slave access point canreceive the combined signal of the lead access point and other slaveaccess points even as it transmits its own signal. It can then convertthis received time domain signal to the frequency domain using a FFT,and perform phase tracking as before using only the OFDM pilotsubcarriers. Since these subcarriers only contain transmission from thelead access point, it allows each slave access point to synchronize itsphase with the lead access point using every data symbol. Further, sincethis scheme does not require resync symbols, it maintains the samepacket format as regular OFDM, and therefore enables unmodified standard802.11 receivers to decode the transmitted packets.

5.2 Diversity Gain

Versions of the system can provide both multiplexing and diversitygains. The description above focusses on multiplexing. The samediscussion applies to diversity except that in this case, we have Naccess points transmitting a data symbol x to a single client. Similarto multiplexing, each access point i computes its channel, h_(i), to theclient. Slave access points also compute the channel from the leadaccess point, and perform distributed phase alignment prior to datatransmission as described in §3. The only difference is that each accesspoint, i, computes its symbol, s_(i) as

$\frac{h_{i}^{*}}{h_{i}}x$

where * is the complex conjugate operator.

5.3 Reciprocity

The distributed coherent system can also allow transmitters to estimatetheir channels to the receivers using receptions at the transmitter fromthe receiver, for example, acknowledgments sent by the receiver inresponse to packet transmission. This allows the distributed coherentsystem to eliminate the overhead from requiring receivers to transmittheir estimates of the forward channel to the transmitters. Theelimination of this overhead allows transmitters to constantly updatechannels from the receiver using packet receptions at transmitters, andthus enables the distributed coherent system to operate even in thepresence of some degree of mobility.

A traditional N-antenna MIMO system in which the uplink and downlinkoperate on the same frequency bands can use channel reciprocity toestimate the forward channel from the transmit antennas to the receiverby using the reverse channel from the receiver to the transmit antennaand multiplying the reverse channel by a complex time-independentcalibration constant. The estimate of the forward channel thus producedis correct up to a time dependent phase offset. In traditional MIMOsystems, this phase offset is the same for all transmit antennas as theyall share the same frequency reference, and hence does not affect theuse of MIMO techniques such as beamforming, nulling etc. Specifically,consider a receiver with frequency offsets of ω^(Master) and ω^(Slave)respectively to a master transmitter and a slave transmitter. LetH_(forw) ^(Master)(t) be the forward channel from the master transmitterto the receiver, and H_(rev) ^(Master)(t) be the reverse channel fromthe receiver to the master transmitter at time t. Let H_(tx) ^(Master)be the channel introduced by the transmit chain at the master which canbe assumed to essentially be time-independent or change very slowly withtime, as it is comprised of the hardware elements on the node. Letθ_(Master)(t) be the phase of the transmitter's oscillator at time t,H_(air,forw) ^(Master)(t) be the passband channel over the air from themaster transmitter to the receiver, H_(rx) ^(Receiver) be the channelintroduced by the receive chain at the receiver, and φ_(Receiver) (t) bethe phase of the receiver's oscillator at time t. Then, since a signalis upconverted at the transmitter, and downconverted at the receiver, wecan express the composite channel H_(forw) ^(master)(t)=H_(tx)^(Master)×H_(air,forw) ^(Master)(t)×H_(rx) ^(Receiver)×e^(j(θ) ^(Master)^((t)-θ) ^(Receiver) ^((t))). Similarly, H_(rev) ^(master)(t)=H_(rx)^(Master)×H_(air,rev) ^(Master)(t)×H_(tx) ^(Receiver)×e^(−j(θ) ^(Master)^((t)-θ) ^(Receiver) ^((t))). By channel reciprocity, H_(air,forw)^(Master)(t)=H_(air,rev) ^(Master)(t). Let the calibration of theforward and reverse channels happen at time t₀, and let K^(Master) bethe corresponding measured calibration constant, which accounts for thedifferences in the channels corresponding to the transmit and receivechains on the transmitter and receiver, such that H_(forw)^(Master)(t₀)=K^(Master)×H_(rev) ^(Master)(t₀)). Due to the frequencyoffset between the master transmitter and the receiver, their oscillatorphases change relative to each other by Δω^(Master)Δt, whereΔω^(Master)=ω^(Receiver)−ω^(Master) and Δt=t−t₀. Thus, we have that(θ_(Receiver)(t)−θ_(Master)(t))=(θ_(Receiver)(t₀)−θ_(Master)(t₀))+Δω^(Master)Δt.Combining with the calibration equation, we therefore have that H_(forw)^(Master)(t)=K^(Master)×H_(rev) ^(Master)(t)×e^(2jΔω) ^(Master) ^(Δt).Similarly, we have that H_(forw) ^(Slave)(t)=K^(Slave)×H_(rev)^(Slave)(t)×e^(2jΔω) ^(Slave) ^(Δt). In the case of a traditional MIMOsystem, where the master transmitter and slave transmitter are driven bythe same clock and frequency reference, Δω^(Master)=Δω^(Slave)=ΔΩ. Inthis case, computing the forward channel from the transmitter to thereceiver by simply multiplying the reverse channel from the receiver tothe transmitter by the calibration constant, i.e., as H_(forw) ^(Master)_(Computed)(t)=K^(Master)×H_(rev) ^(Master)(t) (and similarly for theslave) incurs the same phase error 2ΔΩΔt relative to the actual forwardchannel for all transmitters. MIMO techniques that are only sensitive tothe relative phases between the transmitters at the receiver (forexample, beamforming, nulling), but not the actual phases themselves, donot need to account for this phase difference in the case of traditionalMIMO, as the relative phase between the computed forward channels is thesame as the relative phase between the actual forward channels.

However, in a distributed setting, different transmitters have differentfrequency offsets from the receiver, and hence experience differentphase offsets. As a result, the master transmitter will experience aphase error of 2Δω^(Master)Δt relative to the receiver, and the slavetransmitter will experience a phase error of 2Δω^(Slave)Δt relative tothe receiver. Let the frequency offset between the transmitters,ω^(Slave)−ω^(Master)=Δω. If the transmitters now compute the forwardchannels as before, then the computed forward channels will have adifferent relative phase as compared to the actual forward channels.Specifically, the relative phase between the computed channels, H_(forw)^(Slave) _(Computed)(t)−H_(forw) ^(Master) _(Computed)(t), will differfrom the relative phase between the actual channels, H_(forw) ^(Slave)_(Actual)(t)−H_(forw) ^(Master) _(Actual)(t) by −2ΔωΔt. This will leadto significant degradation in the performance of MIMO techniques if thetraditional mechanism of computing forward channels described above isused.

The distributed coherent system can exploit reciprocity by applying afrequency and phase offset of the received signal at slave transmitterssuch that they emulate the receive oscillator of the master transmitter.They can do this in a manner analogous to the phase and frequency offsetcompensation of the modulated transmission at the slaves. Moreprecisely, at the time of reception of the reverse transmission from thereceiver, the slave transmitter computes its phase offset relative tothe master transmitter. The slave transmitter can do this in a mannersimilar to the computation of phase offset for the forwardtransmission—it can estimate the current phase offset using the phase ofa prior transmission (e.g., data packet or synchronization signal) fromthe master transmitter. As mentioned previously, this phase offset Δψrepresents the value ΔωΔt. The slave can then compute the correctestimate of the forward channel by modulating the received signal bye^(2jΔωΔt)=e^(2jΔψ) prior to decoding and computing the estimate of thereverse channel. The reverse channel thus estimated after this phasecorrection can be used for future coherent transmissions.

This computation of the forward channels from a transmitter bymultiplying the reverse channel estimate by e^(2jΔψ) is accompanied byan update of the reference channel phase (previously defined above asψ(t₀)) between the master transmitter and the slave transmitter. Inother words, this instant can be considered as the t₀ for futuretransmissions. Alternatively, the slave transmitters can multiply thereverse channels by e^(jΔψ) and retain their prior estimate of thereference channel phase between the master transmitter and the slavetransmitter.

In some examples, the forward and reverse channels between a transmitterand receiver pair at some time t are calculated by the followingmechanism. First, the receiver receives a transmission from thetransmitter at time t from the transmitter and evaluates the channelH_(forw)(t) and conveys this information to the transmitter (for e.g. inthe acknowledgement). The receiver then responds with anothertransmission (e.g. an acknowledgement) at time t+δt, where δt is a shorttime duration. The transmitter then evaluates the reverse channelH_(rev)(t+δt) from the receiver. The transmitter can now estimateH_(rev)(t) from H_(rev)(t+δt) by compensating for the carrier frequencydifference Δω, and the sampling frequency difference Δγ, between thetransmitter and receiver accumulated over time δt. This can be done bymodulating the signal received at the transmitter by exp(jδt(Δω+kΔγ)) insubcarrier k. In some implementations, the transmitter can compute thecalibration constant K at time t₀ by obtaining H_(forw)(t₀) andH_(rev)(t₀) using this method and evaluating K=H_(forw)(t₀)/H_(rev)(t₀).The calibration constants for the master and slave transmitters shouldbe computed as if all channels were measured at the same t₀.

To be precise, it is only necessary that all forward channels aremeasured as if they were computed at the same time, and all reversechannels need to be measured as if they were computed at the same timeand all transmitters shared a common oscillator. The time at which theforward channels are measured can be different from the time at whichthe reverse channels are measured. However, for ease of exposition, wewill describe the system here as if all channels are measured at thesame time t₀.

To achieve this effect, a slave transmitter can use a combination of thetechniques described above to correct both forward and reverse channelsfor any phase rotations between t₀ and the time at which the forward andreverse channels for the slave transmitter are measured.

In some cases, the transmitters might desire the exact phase of theforward channel and not simply a rotated version. In such a case, thereceiver can simply include the phase of the forward channel from themaster transmitter to the receiver (or equivalent information such asthe computed frequency offset, from which the phase can be computed bymultiplying by elapsed time and adding to the previous estimate) in itsacknowledgment. The receiver can optionally encode this phase compactlyusing a differential scheme. Specifically, the receiver can communicatea phase θ to a transmitter by transmitting the symbol x₁=x andx₂=xe^(jθ) in different slots (for instance, different in time,frequency or space). The transmitter can then simply recover the value θby computing arg(x₁*x₂), and can perform this same operation for allrelevant subcarriers. As described above, once the master and slavetransmitters emulate a traditional MIMO system in the computation oftheir forward channels, the difference between the phase of the actualforward channel and the phase of the forward channel computed bymultiplying the reverse channel with the calibration factor is preciselythe rotation factor, 2ΔωΔt. The master transmitter can therefore recoverthe rotation factor by subtracting the received value of θ, the actualforward phase, from its computed forward phase. It can communicate therotation factor to all the slaves using its wired backhaul or otherconnectivity. The slaves can then apply this adjustment to their ownforward channel estimate.

In some examples, the transmitters can exchange their updated channelinformation with each other across the wired backhaul or otherconnectivity, and use this updated channel information for one or morefuture packets. The frequency of update can be determined based on therequired tolerance and responsiveness to mobility or other environmentalchanges.

Note that although described in the context of access points that arelinked by wired or wireless channels used to distribute the data that issent to the clients, the approaches may be used in other situations aswell. For example, in a data forwarding situation, a data packet may beforwarded from one set of wireless nodes to a subsequent set of wirelessnodes using a coherent transmission approach described above. Thisprocess can be repeated to reach the destination for the data packet.

Implementations of the approaches may be in software, for example,stored on tangible machine readable media, for controlling processors inthe access points and/or clients. Some implementations may usespecial-purpose hardware (e.g., application specific integratedcircuits) in addition or instead of software.

Other features and advantages of the invention are apparent from thefollowing description, and from the claims.

What is claimed is:
 1. A method for operating a slave transmitter toprovide coordinated transmission with a master transmitter, the methodcomprising: forming a signal for concurrent modulation from the slavetransmitter with a transmission of the signal from the mastertransmitter; maintaining an estimate of a time-varying phase offsetbetween modulation of a transmission from the master and a frequencyreference at the slave access point based on transmissions received atthe slave transmitter from the master transmitter; modifying the signalprior to modulation according to the estimate of the time-varying phaseoffset; and modulating the modified signal according to the frequencyreference at the slave transmitter.
 2. The method of claim 1 wherein atleast one of a modulation frequency and a sampling clock reference areindependent between the master transmitter and the slave transmitter. 3.The method of claim 1 further comprising: concurrently transmitting thesignal modulated at the master transmitter from the master transmitterand the modulated modified signal from the slave transmitter.
 4. Themethod of claim 1 wherein maintaining the estimate of a time-varyingphase offset comprises demodulating a transmission from the mastertransmitter, and comparing the demodulated transmission to expecteddemodulated values.
 5. The method of claim 4 wherein the transmissionfrom the master transmitter comprises a preamble of a transmission ofthe signal from the master transmitter.
 6. The method of claim 4 whereinthe transmission from the master transmitter comprises a frequencymultiplexed transmission, and comparing the demodulated transmission toexpected demodulated values includes performing said comparison atmultiple of the multiplexed frequencies and combining results of thecomparisons.
 7. The method of claim 1 wherein the signal comprises afrequency multiplexed signal, and modifying the signal prior tomodulation comprises modifying each of multiple multiplexed componentsof the signal according to the estimate of the time varying phase. 8.The method of claim 1 wherein forming the signal for transmissionincludes receiving data representing the signal over a communicationlink separate from the transmission system used to transmit the signalfrom the slave transmitter.
 9. A method for estimating a forward channelfrom a slave data transmitter to a data receiver while emulatingcoherent operation with a master transmitter with an independentfrequency and clock reference, the method comprising: utilizingtransmissions from the receiver to the transmitters to determine acomplex multiplicative factor between the forward and reverse channels;maintaining an estimate of a time-varying phase offset betweenmodulation of at transmission from the master and a frequency referenceat the slave access point based on transmissions received at the slavetransmitter from the master transmitter; modifying the received signalfrom the data receiver prior to decoding according to the estimate ofthe time-varying phase offset; decoding the received signal according tothe frequency reference at the slave data transmitter and computing thereverse channel from the data receiver to the slave data transmitter;and computing an estimate of the forward channel by multiplying theestimate of the reverse channel by the computed calibration factor. 10.The method of claim 8 where the estimated forward channels are used byone or more slave transmitters to provide distributed coherenttransmission from multiple wireless transmitters to one or morereceivers.
 11. Software embodied on a tangible computer-readable mediumcomprising instructions for causing a processor associated with a slavetransmitter to provide coordinated transmission with a mastertransmitter by: forming a signal for concurrent modulation from theslave transmitter with a transmission of the signal from the mastertransmitter; maintaining an estimate of a time-varying phase offsetbetween modulation of a transmission from the master and a frequencyreference at the slave access point based on transmissions received atthe slave transmitter from the master transmitter; modifying the signalprior to modulation according to the estimate of the time-varying phaseoffset; and modulating the modified signal according to the frequencyreference at the slave transmitter.
 12. A slave transmitter configuredto provide coordinated transmission with a master transmitter, saidslave transmitter being configured to: form a signal for concurrentmodulation from the slave transmitter with a transmission of the signalfrom the master transmitter; maintain an estimate of a time-varyingphase offset between modulation of a transmission from the master and afrequency reference at the slave access point based on transmissionsreceived at the slave transmitter from the master transmitter; modifythe signal prior to modulation according to the estimate of thetime-varying phase offset; and modulate the modified signal according tothe frequency reference at the slave transmitter.
 13. An apparatuscomprising: a master transmitter including a first oscillator foroperating at a first oscillator frequency, and a first transmittermodule for transmitting symbols, the first transmitter module beingcoupled to the first oscillator for operating at the first oscillatorfrequency; and a slave transmitter, each slave transmitter of the one ormore slave transmitters including a second oscillator which operates ata second oscillator frequency, a receiver module for receivingtransmissions from the master transmitter, the receiver module operatingat the second oscillator frequency and including a frequency offsettracking module for determining a frequency offset between the firstoscillator frequency and the second oscillator frequency based on thetransmissions received from the master transmitter, and a secondtransmitter module for transmitting symbols, the second transmittermodule operating at the second oscillator frequency and including afrequency offset compensation module for compensating for the frequencyoffset before transmitting symbols.
 14. A method for operating one ormore slave transmitters to provide coordinated transmission with amaster access point to a plurality of receivers, the method comprising:loading a plurality of symbols destined for a subset of the plurality ofreceivers into a master symbol storage element coupled to the mastertransmitter; loading the plurality of symbols destined for the subset ofthe plurality of receivers into each of a plurality of slave symbolstorage elements coupled to each of the slave transmitters; maintainingan estimate of a time-varying phase offset between a transmission fromthe master and a frequency reference at each of the slave transmittersbased on transmissions received at the slave transmitters from themaster transmitter; forming a signal for concurrent transmission fromthe one or more slave transmitters with a transmission from the mastertransmitter, forming the signal including combining a plurality ofsub-signals representing the plurality of symbols such that upontransmission of the signal, each sub-signal of the plurality ofsub-signals is present at an antenna of one or more receivers of thesubset of the plurality of receivers and is cancelled at an antenna ofone or more clients of the subset of the plurality of receivers;modifying the signal prior to modulation according to the estimate ofthe time-varying phase offset; and modulating the modified signalaccording to the frequency reference at each of the slave transmitters.15. The method of claim 11 wherein: the plurality of symbols includesdifferent symbols destined for each receiver, and all of the pluralityof symbols intended for the receivers are loaded into the master andslave storage elements; the signals are formed at each of thetransmitters to allow each receiver to simultaneously receive and decodethe symbols destined to it; each receiver then decodes the symbols usingthe combined transmission, such that for each receiver, the combinedtransmission simultaneously achieves a rate substantially equal to therate that receiver would obtain from a single transmission from thetransmitter with the strongest signal to it.
 16. The method of claim 11wherein: the same symbols are loaded into the master storage element andthe slave storage elements, the symbols being destined for a singlereceiver; and the signals are formed at each of the transmitters tocombine with some predictable relative phase at the intended receiver.